On the Selection Function and the Breakage Function in Ball Mill Grinding: Studies on the influence on the two functions of the mill charge and the powder content in the mil feed

The mass balance equation which simulates the comminution process is composed of the selection function and the breakage function. Usually it is assumed that these two functions are independent of grinding time. This means that these two functions are not affected by a change in the size distribution in the mill. These assumptions are studied in this report, especially the influence of the mill charge and that of the powder in a mill upon these functions are investigated. The selection function and the breakage function are obtained from unit grinding data of a series of single size fractions, the single sizes being changed under various feed conditions. The results and discussions are summarized as follows: 1) The selection function decreases as the mill charge increases. This suggests that there may be something like sheltering effect among particles. 2) The breakage function has a tendency to shift to smaller particle size as the mill charge decreases, and then the value of the selection function increases. From these results, it has been shown that with every change of the mill feed, there are intimate relations between these two functions, which will be applicable to the control of mill products. 3) The “cushioning effect” is also confirmed experimentally by using these two functions. An excess of powder in a mill keeps particles from being ground, therefore it affects both the selection function and the breakage function.